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Related papers: Reservoir kernels and Volterra series

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This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…

Numerical Analysis · Mathematics 2024-11-27 Kristof Albrecht , Juliane Entzian , Armin Iske

We consider a distributed system with persistent memory of a type which is often encountered in viscoelasticity or in the study of diffusion processes with memory. The relaxation kernel, i.e. the kernel of the memory term, is scarcely known…

Dynamical Systems · Mathematics 2015-03-16 Luciano Pandolfi

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

Machine Learning · Computer Science 2016-08-22 Ha Quang Minh

This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them. The Tensor Network Kalman filter also easily accommodates the case where…

Systems and Control · Computer Science 2016-10-19 Kim Batselier , Zhongming Chen , Ngai Wong

We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…

Functional Analysis · Mathematics 2025-11-18 James Tian

Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced…

Quantum Physics · Physics 2026-02-25 Lukas Gonon , Rodrigo Martínez-Peña , Juan-Pablo Ortega

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal,…

Neural and Evolutionary Computing · Computer Science 2018-08-28 Lyudmila Grigoryeva , Juan-Pablo Ortega

We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto…

Emerging Technologies · Computer Science 2015-04-27 Ozgur Yilmaz

This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…

Machine Learning · Computer Science 2021-07-16 Mohammad Mahdi Derakhshani , Xiantong Zhen , Ling Shao , Cees G. M. Snoek

Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely…

Optimization and Control · Mathematics 2026-03-20 Anh-Tuan Clabaut , Jean Auriol , Islam Boussaada , Guilherme Mazanti

The Volterra series is a powerful tool in modelling a broad range of nonlinear dynamic systems. However, due to its nonparametric nature, the number of parameters in the series increases rapidly with memory length and series order, with the…

Signal Processing · Electrical Eng. & Systems 2018-04-23 Jeremy G. Stoddard , James S. Welsh

The paper is a follow-up of the recently introduced kernel-based framework to identify nonlinear input-output systems regularized by desirable input-output incremental properties. Assuming that the system has fading memory, we propose to…

Systems and Control · Electrical Eng. & Systems 2025-11-14 Yongkang Huo , Thomas Chaffey , Rodolphe Sepulchre

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…

Functional Analysis · Mathematics 2008-07-11 C. Carmeli , E. De Vito , A. Toigo , V. Umanità

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep…

Machine Learning · Statistics 2021-02-18 Jonathan Dong , Ruben Ohana , Mushegh Rafayelyan , Florent Krzakala

This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering…

Emerging Technologies · Computer Science 2015-10-08 Lyudmila Grigoryeva , Julie Henriques , Juan-Pablo Ortega

Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional…

Soft Condensed Matter · Physics 2026-01-12 Veit-Lorenz Heuthe , Lukas Seemann , Samuel Tovey , Clemens Bechinger

The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum…

Quantum Physics · Physics 2024-05-24 Aoi Hayashi , Akitada Sakurai , Shin Nishio , William J. Munro , Kae Nemoto

Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the…

Machine Learning · Computer Science 2023-04-04 Lukas Gonon , Lyudmila Grigoryeva , Juan-Pablo Ortega

Quantum reservoir computing has emerged as a promising paradigm within the field of quantum machine learning, harnessing the inherent properties of quantum systems to optimise and enhance information processing capabilities. Here, we…

Quantum Physics · Physics 2025-09-03 Adam Burgess , Marian Florescu

This study introduces an approach for modeling unsteady transonic aerodynamics within a parametric space, using Volterra series to capture aerodynamic responses and machine learning to enable interpolation. The first- and second-order…

Computational Engineering, Finance, and Science · Computer Science 2024-10-28 Gabriele Immordino , Andrea Da Ronch , Marcello Righi